EECE7201_HW03_v02 (1)

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EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 1 Module TWO: Semiconductor Fundamental Part 2 Homework Set 03 Release Date: 02/19/2024 Homework Instructions: a. Homework set 03 is due on: 03/11/2024 - 11:59 pm b. If an extension is needed, the request must be submitted 48 hours before the deadline directly to the instructor’s email. The extensions are subject to the instructor’s decision and, if granted, will be for the entire class. c. Late submission is allowed, with the reductions (-30% /extra day). d. Solutions: scanned/e-ink solutions must be submitted to the Canvas drop box. e. Format: Use this page and add solutions (e-ink/typed/scanned) directly to this page. Out-of- format HWs will not be graded and will be returned for correction with deductions (-30% /extra day). f. In using paper, only one side of the paper for the answers to enhance the quality of the scans. Insert white pages when needed and make sure pages are in order in the scanned file. g. The homework problems are individual activities, and collaborations are prohibited. Note: Assume that all impurities are ionized and unless otherwise specified, assume T = 300 K. Physical constants for some common semiconductors can be found in Appendix A. Final G rade: ………………………………………………. Class Median: ………..…………………………………… Comments: ………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………………………… Student Name: …………………..……………………………
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 2 HW 3.01: Problem 3.2-3 Calculate conductivity for silicon at room temperature under each of the following doping conditions: a. N D = 10 18 cm 3 b. N A = 5 × 10 16 cm 3 c. N D = 2 × 10 19 cm 3 d. Calculate the resistivity for each case above.
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 3 HW 3.02: Problem 3.6 Consider a sample of silicon doped with N D = 5 × 10 19 cm 3 having dimensions 0.10 μm × 0.85 μm × 65 nm. One volt is applied across the thinnest dimension. Find the current produced, and the corresponding current density. These dimensions could represent the current-conducting channel of a field-effect transistor.
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EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 4 HW 3.03: Problem 3.15 A bar of silicon of 1 cm in length is uniformly doped with 1.0 × 10 16 cm 3 phosphorus atoms. A voltage of 2.0 V is applied across the bar. Find: a. the electron drift current density b. the hole drift current density
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 5 HW 3.04: Problem 3.17 The electron velocity in Si has its saturation value ( ʋ sat ≈ 1 × 10 7 cm/s) over the range of 5 × 10 4 to 2 × 10 5 V/cm. Plot the (a) mobility- field (μ − ) and (b) t relations over this range of fields. Note: use a computer program such as MATLAB, Python, Mathematica, for the plot(s). The plotting script must be attached as readable text (selectable text to copy and paste).
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 6
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EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 7 HW 3.05: Problem 3.19 The excess electron concentration in a semiconductor varies as Δn(x) = 1 20 10 μm x e . Find the electron diffusion current at x = 0.5 μm. Let D n = 35 cm 2 /s. Sketch the carrier concentration as a function of position, and label the directions of electron flow and electron current. Note: use a computer program such as MATLAB, Python, Mathematica, for the plot(s). The plotting script must be attached as readable text (selectable text to copy and paste).
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 8
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 9 HW 3.06: Problem 3.20 A sample of silicon is doped such that the electron concentration varies linearly across the sample. The sample is 0.5 mm thick. The donor concentration varies from N D = 0 at x = 0 to N D = 10 16 cm 3 at x = 0.5 μ m. a. Write equations for n ( x ) and p ( x ). b. Find the electron diffusion current density. c. Find the hole diffusion current density at x = 0 and x = 0.5 μ m. Can the minority carriers contribute significant diffusion current? d. Find an expression for E C ( x ) − E f as a function of x . Sketch the energy band diagram. (The Fermi level is constant at equilibrium, so draw the Fermi level as a flat line and adjust E C E f appropriately.) e. At equilibrium, the total current must be zero. Show that there must therefore be an internal electric field present in this sample. (The field is generated by the variation in doping, as we will see in the next chapter.)
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EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 10
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 11 HW 3.07: Problem 3.22 A sample of intrinsic GaN is illuminated with a 10 mW/cm 2 beam of light at the blue edge of what people can see, λ = 300 nm. The electron lifetime is 2 ps. The electron mobility for intrinsic GaN is about 400 cm 2 /V s and hole mobility is about 100 cm2/V s. a. What is the number of photons arriving at the semiconductor surface per sec? ( Recall energy = power × time. ) b. Verify that photons of this energy can be absorbed. c. Assuming every photon is absorbed and creates an electron-hole pair, and assuming the GaN sample is 1 mm thick, what is the optical generation rate? d. What are the equilibrium electron and hole densities (in the dark)? e. What are the excess carrier concentrations when the light is on? f. What are the recombination rates for electrons and for holes when the light is off? When the light is on? g. What are the steady-state carrier densities n and p? h. How much does the conductivity of this sample change compared with its dark value? i. Suppose the power level is kept the same, but the wavelength of the light is shifted to the red edge of human vision (λ = 700 nm). What is the generation rate now?
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 12
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EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 13
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 14 HW 3.08: Problem 3.24 A direct gap semiconductor sample is illuminated at one end with light of λ = 500 nm (green), with an intensity of 5.0 mW/cm 2 . The area of the illuminated surface is 0.80 cm 2 . Assume the carrier lifetimes are 10 ns. a. Find the number of photons striking the sample per second. b. If every photon is absorbed uniformly (with x) within 1 μm of the surface, what are the excess carrier concentrations Δn and Δp in this region?
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 15 HW 3.09: Problem 3.26 Consider a bar of semiconductor illuminated as shown in Figure P3.1. a. Sketch the concentrations of electrons and holes as functions of position. b. In which direction(s) will the electrons diffuse? Holes? c. In what directions do the electron and hole diffusion currents go? d. Explain why a plot of voltage versus position along the length of the sample is as shown in the figure.
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EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 16
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 17
EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 18 HW 3.10: Problem 3.29 A sample of InP is doped such that E f E V = 0.3 eV. It is also illuminated such that Δ n = Δ p = 10 3 cm 3 . Find the quasi Fermi levels and sketch the energy band diagram. Repeat for Δ n = Δ p = 10 10 .
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EECE7201 - Home Work Set 03 Spring 2024 EECE 7201 Solid State Device (Spring 2024) pg. 19